Properties

Label 7497.j
Number of curves 2
Conductor 7497
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("7497.j1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 7497.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
7497.j1 7497f2 [0, 0, 1, -26166, -1630022] [] 13824  
7497.j2 7497f1 [0, 0, 1, 294, -9347] [] 4608 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 7497.j have rank \(1\).

Modular form 7497.2.a.j

sage: E.q_eigenform(10)
 
\( q - 2q^{4} + 3q^{5} + 3q^{11} + q^{13} + 4q^{16} - q^{17} + q^{19} + O(q^{20}) \)

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.